MCQ
Let $f: R \rightarrow R$ be defined as
$f(x)=\left[\begin{array}{ll}{\left[e^{x}\right],} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,x<0 \\ a e^{x}+[x-1], \,\,\,\,\,\,\,\,\,0 \leq x<1 \\ b+[\sin (\pi x)], \,\,\,\,\,\,\,\,\,\,\,\,1 \leq x<2 \\ {\left[e^{-x}\right]-c,} \,\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\,\,\,\,\,\,x \geq 2\end{array}\right.$
where a,b,c $\in R$ and $[t]$ denotes greatest integer less than or equal to $t.$ Then, which of the following statements is true $?$
- AThere exists $a,b,c$ $\in R$ such that $f$ is continuous of $R$.
- BIf $f$ is discontinuous at exactly one point, then $a+b+c=1$
- ✓If $f$ is discontinuous at exactly one point, then $a+b+c \neq 1$
- D$f$ is discontinuous at atleast two points, for any values of $a , b$ and $c$.